We are attempting to develop a mathematical model that will enable us to describe the level of cyclic AMP (cAMP) in various types of cultured cells in quantitative terms, in the presence and absence of agonists, as a function of the concentration of agonist and of the time after the agonist has been added, under a variety of experimental conditions. The three factors which are most important in determining the level of cAMP are: 1) adenylyl cyclase (AC) activity, which chan be increased as a result of the agonist-receptor interaction; 2) the activity of phosphodiesterase (PDE); and 3) the rate of efflux out of the cell. The agonist-receptor interaction leads not only to AC activation but also to tachyphylaxis. The model developed to this point is adequate for describing AC activation in membrane preparations and can qualitatively account for the time-course of cAMP accumulation in intact cells. Attempts to simulate experimental data exactly, however, led to the recognition that PDE is regulated in intact cells in a complex manner, and that it must be much more active at low cAMP levels than at high. This led us to develop a new theory of how PDE is regulated, which in turn enabled us to develop a new method for studying and characterizing the properties of this enzyme. In brief summary, PDE is postulated to exist in 2 forms; cAMP interacts with the high activity form (P1) to produce a less active form (P2). The system is characterized by four rate constants (one for the rate of formation of P2 from P1 and cAMP, another for the rate of dissociation of cAMP from P2, and two to characterize the activities of P1 and P2). We are currently attempting to measure these constants so that we can utilize them in a model that will be applicable to intact cells. A second specific aim is to measure PDE activity in intact cells by an independent method based on the incorporation of H2O into 5'AMP as a result of hydrolytic cleavage. We are at the same time trying to refine the AC part of the model to include additional biochemical details, including especially the role of a guanine nucleotide-binding protein which interacts with both the receptor and the catalytic component of AC. A final specific aim is to develop m,onoclonal antibodies to this protein. These antibodies should be useful as tools for quantitative studies of this protein.